Question

On a horizontal plane there is a vertical tower with a flag pole on the top of the tower. At a point 9 metres away from the foot of the tower the angle of elevation of the top and bottom of the flag pole are ${60}^{\circ }and{30}^{\circ }$ respectively. Find the height of the tower and the flag pole mounted on it.

Answer 1

let the height of the tower be h m. and height with flag stuff be h+5 m

base be x m

then

$tan30=\frac{h}{x}$

$\frac{1}{\sqrt{3}}=\frac{h}{x}$

$x=\sqrt{3}h$ -----(1)

$tan60=\frac{h+5}{x}$

$\sqrt{3}=\frac{h+5}{x}$

$x=\frac{h+5}{\sqrt{3}}$ -----(2)

from (1) & (2)

$\sqrt{3}h=\frac{h+5}{\sqrt{3}}$

$h=2.5m$